PLEASE I NEED SOMEONE TO HELP MY ASSIGNMENT, DUE IS TOMMOROW. (´;︵;`)​

Step-by-step explanation:

A) In ΔONE & ΔEST

            ON // ST   (Construction) and NS is transversal.

            ∠1 = ∠4   {alternate interior angles}

            NE =ES      {Given E is midpoint}

        ∠2  =  ∠3       {Vertically opposite angle}

   ΔONE ≅ ΔEST  { A S A congruent}

  OE ≅  TE  {CPCT}

  ON = ST {CPCT}  (I)

ON = OH (II)

From (I) & (II)

OH = ST    & OH // ST (construction)

OHST is a parallelogram.

So,  OE // HS  (A)

       OE = TE

OT = 2OE

OE = (1/2)OT

OE = (1/2)HS    (B)

From A & B , midpoint theorem is proved